NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm （MCRDA）, is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.

An improved cut-based recursive decomposition algorithm for reliability analysis of networks

In this paper, an improved cut-based recursive decomposition algorithm is proposed for lifeline networks. First, a complementary structural function is established and three theorems are presented as a premise of the proposed algorithm. Taking the minimal cut of a network as decomposition policy, the proposed algorithm constructs a recursive decomposition process. During the decomposition, both the disjoint minimal cut set and the disjoint minimal path set are simultaneously enumerated. Therefore, in addition to obtaining an accurate value after decomposing all disjoint minimal cuts and disjoint minimal paths, the algorithm provides approximate results which satisfy a prescribed error bound using a probabilistic inequality. Two example networks, including a large urban gas system, are analyzed using the proposed algorithm. Meanwhile, a part of the results are compared with the results obtained by a path-based recursive decomposition algorithm. These results show that the proposed algorithm provides a useful probabilistic analysis method for the reliability evaluation of lifeline networks and may be more suitable for networks where the edges have low reliabilities.

An Improved Heuristic Recursive Strategy Based on Genetic Algorithm for the Strip Rectangular Packing Problem

与基因算法结合的改进启发式的递归的策略在这份报纸被介绍。第一，这个方法寻找一些矩形，它有一样的长度或宽度，到没有浪费空间，形成一些层，然后，计算留下包装顺序的高度使用启发式的递归的策略并且使用基因算法的进化能力减少高度。基准问题的几个班上的计算结果证明了介绍算法能与已知的进化启发规则竞争。它特别为大测试问题更好表现。

A New Recursive Parameter Estimation Algorithm of Multi－Variable Time－Varying AR Model

A new recursive algorithm of multi variable time varying AR model is proposed. By changing the form of AR model, the parameter estimation can be regarded as state estimation of state equations. Then the Kalman filter is used to estimate the variation of

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.

BLOCK ADAPTIVE RECURSIVE ALGORITHM FOR VIDEO CONFERENCE CODING

This paper presents a new motion estimation algorithm for video conference signal coding. This type of algorithm is called block adaptive recursive algorithm (BARA). Simulation results show that this new algorithm has better performance than conventional ones.

REESSE Unified Recursive Algorithm for Solving Three Computational Problems

Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.

RECURSIVE ALGORITHM FOR ADAPTIVE ARRAYS AND SYSTOLIC ARRAY IMPLEMENTATION

In this paper, a new recursive algorithm of adaptive array weight vectors and its systolic array implementing structure is proposed, which is based on the QR decomposition algorithms and the idea of algorithmic engineering. The algorithm can realize fully parallel and pipeline processing.

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

Recursive Algorithm Based Reliability Analysis of Multiphase Satellite Systems with Propagated Failures

Modern satellite systems are generally designed to fulfill multiphase-missions. Component /subsystem redundancies are commonly used to achieve high reliability and long life of modern satellite systems. These characteristics have leaded to a critical issue of reliability analysis of satellites that is how to deal with the reliability analysis with multiphase-missions and propagated failures of redundant components. Traditional methods based on the binary decision diagram( BDD) can hardly cope with these issues efficiently. Accordingly, a recursive algorithm method was introduced to facilitate the reliability analysis of satellites. This method was specified for the analysis of static fault tree and it was implemented by generating combination of component failures and carrying out a backward recursive algorithm. The effectiveness of the proposed method was demonstrated through the reliability analysis of a multiphase satellite system with propagated failures.The major advantage of the proposed method is that it does not need composition of BDD and its computational process is automated.

A Recursive Algorithm on Rational Interpolation

In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.

Recursive Algorithm and Alternate Operation Strategy in Sequential Tests

Based on the sequential probability ratio test(SPRT)developed by Wald,an improved method for successful probability test of missile flight is proposed.A recursive algorithm and its program in Matlab are designed to calculate the real risk level of the sequential test decision and the average number of samples under various test conditions.A concept,that is "rejecting as soon as possible",is put forward and an alternate operation strategy is conducted.The simulation results show that it can reduce the test expenses.

The Application Research of a Fast Recursive Predictive Algorithm on Medical X-ray Image Compression

This paper studied a fast recursive predictive algorithm used for medical X-ray image compression. This algorithm consists of mathematics model building, fast recursive algorithm deducing, initial value determining, step-size selecting, image compression encoding and original image recovering. The experiment result indicates that this algorithm has not only a higher compression ratio to medical X-ray images compression, but also promotes image compression speed greatly.

Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization

Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.